Understanding Bandpass Filtering and Its Effects on Signal Frequency

[Granger]

Homework Statement

So let's say that I have a signal of fundamental frequency 50Hz. I then have a band-pass filter that passes the band between 800 and 1000 Hz of my signal. I don't know the expression of the signals I just know the graphics:

[![enter image description here][1]][1] [1]: https://i.stack.imgur.com/bwfxN.png

Homework Equations

3. The Attempt at a Solution [/B]
My question now is how should I determine the frequency of the sinusoidals that have resulted by processing the signal.
I know that the output signal has this sinusoidal aspect because every function is a sum of different frequencies sinusoidals and that the pass-band frequency is only passing some frequencies i.e. some sinusoidals.
I know they might be related with the frequency of the original signal but I'm not sure. Can anybody help me? Thanks.

 

[scottdave]

You need to determine the Fourier series for your input signal, then determine which of these fall into the band. Is this an ideal bandpass filter?

 

[Granger]

You need to determine the Fourier series for your input signal, then determine which of these fall into the band. Is this an ideal bandpass filter?

Hello scottdave! The thing is I don't have an expression for my input signal, only knowing its fundamental frequency. Nothing is said about the filter not being ideal so I assume that yes it is ideal.

 

[scottdave]

The blue signal is what I think you are talking about. Upon closer look, it appears to be a sine wave amplitude 0.5 added to a square wave 0.5 amplitude. Take a look at this link or others to see about the components of a square wave.
http://lpsa.swarthmore.edu/Fourier/Series/ExFS.html
what is the green signal?

 

[Granger]

The blue signal is what I think you are talking about. Upon closer look, it appears to be a sine wave amplitude 0.5 added to a square wave 0.5 amplitude. Take a look at this link or others to see about the components of a square wave.
http://lpsa.swarthmore.edu/Fourier/Series/ExFS.html
what is the green signal?

The blue signal is the input signal. The green signal is the output signal, and it's the one in which we're trying to determine the frequency of the sinusoids.

 

[scottdave]

Count the number of peaks of the green signal which occur in one cycle of the blue signal. As a hint - square waves consist only of odd harmonics.
So for example if an output signal had 5 peaks over 1 cycle of 50 Hz then that signal has a frequency of 5 × 50 Hz = 250 Hz.

 

[Granger]

Count the number of peaks of the green signal which occur in one cycle of the blue signal. As a hint - square waves consist only of odd harmonics.
So for example if an output signal had 5 peaks over 1 cycle of 50 Hz then that signal has a frequency of 5 × 50 Hz = 250 Hz.

By peaks do you mean just maxima?
I'm sorry that isn't make sense to me.Why does that work? Also I tried to do what you said and got for all of them 100 Hz (2 peaks for the maximum wave) which doesn't make sense...

 

[Granger]

I do understand we will only have odd harmonics because we have an odd function...

 

[scottdave]

Yes by peaks, mean maxima. From one maxima to the next is a wavelength. what is it you were counting to multiply by 100 Hz? What answer did you get? You could also just count a specific number of cyxles, then divide by the time period covered to get cycles per second.

 

[scottdave]

I do understand we will only have odd harmonics because we have an odd function...

Could you elaborate on your definition of "odd function"? I think of even as like a cosine where there is symmetry across y axis.
Odd has f (-x) = -f (x), like sine. A function with odd harmonics is determined by the shape of the wave.
Were you able to arrive at an answer for the problem?

 

[scottdave]

Ha. I meant y axis, not 6. My phone is not letting me go and edit my post, though. (it is fixed, now)

 

[donpacino]

Frequency = 1/period

Find the period of the sinusoid and invert it to find frequency

 

[donpacino]

Also since your plot looks like it is in matlab, you can check your work by doing an fft on the data

Y = fft(X)

 

[scottdave]

Also since your plot looks like it is in matlab, you can check your work by doing an fft on the data

Y = fft(X)

I think maybe @Granger does not have access to the data points, just an image of the graph.

I wonder if maybe I confused the issue with the "odd harmonics"

Here are some things to think about.
While the square wave does produce only odd harmonics (multiples of the base wave), something interesting will happen in this situation. Which harmonics can be present in the filter pass band?
Do you see what is going on with the output? What happens with two sine waves of different frequencies? You may find the following helpful:
https://en.wikipedia.org/wiki/Beat_(acoustics) and http://hyperphysics.phy-astr.gsu.edu/hbase/Sound/beat.html#c3

While they talk about sound, similar effects can occur with other types of waves.